76 research outputs found
Schwinger-Dyson Equation for Supersymmetric Yang-Mills Theory
We study our Schwinger-Dyson equation as well as the large loop
equation for supersymmetric Yang-Mills theory in four dimensions by the N=1
superspace Wilson-loop variable. We are successful in deriving a new manifestly
supersymmetric form in which a loop splitting and joining are represented by a
manifestly supersymmetric as well as supergauge invariant operation in
superspace. This is found to be a natural extension from the abelian case. We
solve the equation to leading order in perturbation theory or equivalently in
the linearized approximation, obtaining a desirable nontrivial answer. The
super Wilson-loop variable can be represented as the system of one-dimensional
fermion along the loop coupled minimally to the original theory. One-loop
renormalization of the one-point Wilson-loop average is explicitly carried out,
exploiting this property. The picture of string dynamics obtained is briefly
discussed.Comment: 47 pages, late
The Quiver Matrix Model and 2d-4d Conformal Connection
We review the quiver matrix model (the ITEP model) in the light of the recent
progress on 2d-4d connection of conformal field theories, in particular, on the
relation between Toda field theories and a class of quiver superconformal gauge
theories. On the basis of the CFT representation of the beta deformation of the
model, a quantum spectral curve is introduced as << det (x- i g_s \partial
\phi(z)) >>=0 at finite N and for beta \neq 1. The planar loop equation in the
large N limit follows with the aid of W_n constraints. Residue analysis is
provided both for the curve of the matrix model with the "multi-log" potential
and for the Seiberg-Witten curve in the case of SU(n) with 2n flavors, leading
to the matching of the mass parameters. The isomorphism of the two curves is
made manifest.Comment: 37 pages; v2: version to appear in Prog. Theor. Phys. Title changed.
Isomorphism of the SU(n) spectral curve and the SW curve of Witten-Gaiotto
form as well as the matching of the mass parameters more fully give
-Virasoro/W Algebra at Root of Unity and Parafermions
We demonstrate that the parafermions appear in the -th root of unity limit
of -Virasoro/ algebra. The proper value of the central charge of the
coset model is given
from the parafermion construction of the block in the limit.Comment: 13 pages, 1 figure; v2: references added, minor corrections mad
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